The Universe of Discourse

Fri, 21 Aug 2015

A message to the aliens, part 6/23 (chemistry)

Earlier articles: Introduction Common features Page 1 (numerals) Page 2 (arithmetic) Page 3 (exponents) Page 4 (algebra) Page 5 (geometry)

This is page 6 of the Cosmic Call message. An explanation follows.

The 10 digits again:











Page 6 discusses fundamental particles of matter, the structure of the hydrogen and helium atoms, and defines glyphs for the most important chemical elements.

Depicted at top left is the hydrogen atom, with a proton in the center and an electron circulating around the outside. This diagram is equated to the glyph for hydrogen.

The diagram for helium is similar but has two electrons, and its nucleus has two protons and also two neutrons.




The illustrations may puzzle the aliens, depending on how they think of atoms. (Feynman once said that this idea of atoms as little solar systems, with the elctrons traveling around the nucleus like planets, was a hundred years old and out of date.) But the accompanying mass and charge data should help clear things up. The first formula says

!!M_p = 1836\cdot M_e!!

the mass of the proton is 1836 times the mass of the electron, and that 1836, independent of the units used and believed to be a universal and fundamental constant, ought to be a dead giveaway about what is being discussed here.

If you want to communicate fundamental constants, you have a bit of a problem. You can't tell the aliens that the speed of light is !!1.8\cdot10^{12}!! furlongs per fortnight without first explaining furlongs and fortnights (as is actually done on a later page). But the proton-electron mass ratio is dimensionless; it's 1836 in every system of units. (Although the value is actually known to be 1836.15267; I don't know why a more accurate value wasn't given.)

This is the first use of subscripts in the document. It also takes care of introducing the symbol for mass. The following formula does the same for charge : !!Q_p = -Q_e!!.

The next two formulas, accompanying the illustration of the helium atom, describe the mass (1.00138 protons) and charge (zero) of the neutron. I wonder why the authors went for the number 1.00138 here instead of writing the neutron-electron mass ratio of 1838 for consistency with the previous ratio. I also worry that this won't be enough for the aliens to be sure about the meaning of . The 1836 is as clear as anything can be, but the 0 and -1 of the corresponding charge ratios could in principle be a lot of other things. Will the context be enough to make clear what is being discussed? I suppose it has to; charge, unlike mass, comes in discrete units and there is nothing like the 1836.

The second half of the page reiterates the symbols for hydrogen and helium and defines symbols for eight other chemical elements. Some of these appear in organic compounds that will be discussed later; others are important constitutents of the Earth. It also introduces symbol for “union” or “and”: . For example, sodium is described as having 11 protons and 12 neutrons.











Most of these new glyphs are not especially mnemonic, except for hydrogen—and aluminium, which is spectacular.

The blog is going on hiatus until early September. When it returns, the next article will discuss page 7, shown at right. It has three errors. Can you find them? (Click to enlarge.)

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Wed, 19 Aug 2015

A message to the aliens, part 5/23 (geometry)

Earlier articles: Introduction Common features Page 1 (numerals) Page 2 (arithmetic) Page 3 (exponents) Page 4 (algebra)

This is page 5 of the Cosmic Call message. An explanation follows.

The 10 digits again:











Page 5 discusses two basic notions of geometry. The top half concerns circles and introduces !!\pi!!. There is a large circle with its radius labeled :

The outer diameter is then which is !!2\cdot r!!.

The perimeter is twice times the radius , and the area is times the square of the radius squared. What is ? It's !!\pi!! of course, as the next line explains, giving !!\pi = 3.1415926545697932…365698614212904!!, which gives enough digits on the front to make clear what is being comunicated. The trailing digits are around the 51 billionth places and communicate part of the state of our knowledge of !!\pi!!. I almost wish the authors had included a sequence of fifteen random digits at this point, just to keep the aliens wondering.

The bottom half of the page is about the pythagorean theorem. Here there's a rather strange feature. Instead of using the three variables from the previous page, , the authors changed the second one and used instead. This new glyph does not appear anywhere else. A mistake, or did they do it on purpose?

In any case, the pythagorean formula is repeated twice, once with exponents and once without, as both !!z^2=x^2+b^2!! and !!z\cdot z = x\cdot x + b\cdot b!!. I think they threw this in just in case the exponentiation on the previous pages wasn't sufficiently clear. I don't know why the authors chose to use an isosceles right triangle; why not a 3–4–5 or some other scalene triangle, for maximum generality? (What if the aliens think we think the pythagorean theorem applies only for isosceles triangles?) But perhaps they were worried about accurately representing any funny angles on their pixel grid. I wanted to see if it would fit, and it does. You have to make the diagram smaller, but I think it's still clear:

(I made it smaller than it needed to be and then didn't want to redo it.)

I hope this section will be sufficiently unmistakable that the aliens will see past the oddities.

The next article will discuss page 6, shown at right. (Click to enlarge.) Try to figure it out before then.

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Mon, 17 Aug 2015

A message to the aliens, part 4/23 (algebra)

Earlier articles: Introduction Common features Page 1 (numerals) Page 2 (arithmetic) Page 3 (exponents)

This is page 4 of the Cosmic Call message. An explanation follows.

Reminder: page 1 explained the ten digits:











And the equal sign . Page 2 explained the four basic arithmetic operations and some associated notions:






ellipsis (…)



This page, headed with the glyph for “mathematics” , describes the solution of simple algebraic equations and defines glyphs for three variables, which we may as well call !!x,y,!! and !!z!!:




Each equation is introduced by the locution which means “solve for !!x!!”. This somewhat peculiar “solve” glyph will not appear again until page 23.

For example the second equation is !!x+4=10!!:

Solve for !!x!!: !!x+4=10!!

The solution, 6, is given over on the right:


After the fourth line, the equations to be solved change from simple numerical equations in one variable to more abstract algebraic relations between three variables. For example, if

Solve for !!x!!: !!x\cdot y=z!!


!!x=z\div y!!.

The next-to-last line uses a decimal fraction in the exponent, !!0.5!!: . On the previous page, the rational fraction !!1\div 2!! was used. Had the same style been followed, it would have looked like this: .

Finally, the last line defines !!x=y^3!! and then, instead of an algebraic solution, gives a graph of the resulting relation, with axes labeled. The scale on the axes is not the same; the !!x!!-coordinate increases from 0 to 20 pixels, but the !!y!!-coordinate increases from 0 to 8000 pixels because !!20^3 = 8000!!. If axes were to the same scale, the curve would go up by 8,000 pixels. Notice that the curve does not peek above the !!x!!-axis until around !!x=8, y=512!! or so. The authors could have stated that this was the graph of !!y=x^3\div 400!!, but chose not to.

I also wonder what the aliens will make of the arrows on the axes. I think the authors want to show that our coordinates increase going up and to the left, but this seems like a strange and opaque way to do that. A better choice would have been to use a function with an asymmetric graph, such as !!y=2^x!!.

(After I wrote that I learned that similar concerns were voiced about the use of a directional arrow in the Pioneer plaque.

(Wikipedia says: “An article in Scientific American criticized the use of an arrow because arrows are an artifact of hunter-gatherer societies like those on Earth; finders with a different cultural heritage may find the arrow symbol meaningless.”)

The next article will discuss page 5, shown at right. (Click to enlarge.) Try to figure it out before then.

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Fri, 14 Aug 2015

A message to the aliens, part 3/23 (exponentiation)

Earlier articles: Introduction Common features Page 1 (numerals) Page 2 (arithmetic)

This is page 3 of the Cosmic Call message. An explanation follows.

Reminder: page 1 explained the ten digits:











And the equal sign . Page 2 explained the four basic arithmetic operations and some associated notions:






ellipsis (…)



This page, headed with the glyph for “mathematics” , explains notations for exponentiation and scientific notation. (This notation was first used on page 1 in the mersenne prime .)

Exponenentiation could be represented by an operator, but instead the authors have chosen to represent it by a superscripted position on the page, as is done in conventional mathematical notation. This saves space.

The top section of the page has small examples of exponentiation, including for example !!5^3=125!!:


There is a section that follows with powers of 10: !!10^1=10, 10^2=100, 10^3=1000, !! and more interestingly !!10^{{}^-2} = 0.01!!:

!!10^{{}^-2} = 0.01!!

This is a lead-in to the next section, which expresses various quantities in scientific notation, which will recur frequenly later on. For example, !!0.045!! can be written as !!45\times 10^{{}^-2}!!:

!!45\times10^{{}^-2} = 0.45!!

Finally, there is an offhend remark about the approximate value of the square root of 2:

!!2^{1\div 2} = 1.41421356…!!

The next article will discuss page 4, shown at right. (Click to enlarge.) Try to figure it out before then.

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Wed, 12 Aug 2015

A message to the aliens, part 2/23 (arithmetic)

Earlier articles: Introduction Common features Page 1 (numerals)

This is page 2 of the Cosmic Call message. An explanation follows.

Reminder: the previous page explained the ten digits:











This page, headed with the glyph for “mathematics” , explains the arithmetic operations on numbers.

The page is in five sections, three on top and two below.
The first four sections explain addition , subtraction , multiplication , and division . Each is explained with a series of five typical arithmetic equalities. For example, !!4\times 3= 12!!:

The subtraction sign actually appeared back on page 1 in the Mersenne prime !!2^{3021377}-1!! .

The negative sign is introduced in connection with subtraction, since !!1-2={}^-1!!:

Note that the negative-number sign is not the same as the subtraction sign.

The decimal point is introduced in connection with division. For example, !!3\div 2 = 1.5!!:

There is also an attempt to divide by zero:

It's not clear what the authors mean by this; the mysterious glyph does not appear anywhere else in the document. What did they think it meant? Infinity? Indeterminate? Well, I found out later they published a cheat sheet, which assigns the meaning “undetermined” to this glyph. Not a great choice, in my opinion, because !!1÷0!! is not numerically equal to anything.

For some reason, perhaps because of space limitations, the authors have stuck the equation !!0-1 = {}^-1!! at the bottom of the division section.

The fifth section, at lower right, displays some nonterminating decimal fractions and introduces the ellipsis or ‘…’ symbol. For example, !!1\div 9 = 0.1111\ldots!!:

I would have put !!2÷27 = 0.0740…!! here instead of !!2\div 3!!, which I think is too similar to the other examples.

The next article, to appear 2015-08-14, will discuss page 3, shown at right. (Click to enlarge.) Try to figure it out before then.

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A message to the aliens, part 1/23 (numbers)

Earlier articles: Introduction Common features

This is page 1 of the Cosmic Call message. An explanation follows.

This page, headed with the glyph for “mathematics” , explains the numeral symbols that will be used throughout the rest of the document. I should warn you that these first few pages are a little dull, establishing basic mathematical notions. The good stuff comes a little later.

The page is in three sections. The first section explains the individual digit symbols. A typical portion looks like this:

•••• ••• = 0111 = 7

Here the number 7 is written in three ways: first, as seven dots, probably unmistakeable. Second, as a 4-bit binary number, using the same bit symbols that are used in the page numbers. The three forms are separated by the glyph , which means “equals”. The ten digits, in order from 0 to 9, are represented by the glyphs











The authors did a great job selecting glyphs that resemble the numerals they represent. All have some resemblance except for 4, which has 4 horizontal strokes. Watch out for 4; it's easy to confuse with 3.

The second section serves two purposes. It confirms the meaning of the ten digits, and it also informs the aliens that the rest of the message will write numerals in base ten. For example, the number 14:

••••• ••••• •••• = 14

Again, there are 14 dots, an equal sign, and the numeral 14, this time written with the two glyphs (1) and (4). The base-2 version is omitted this time, to save space. The aliens know from this that we are using base 10; had it been, say, base 8, the glyphs would have been .

People often ask why the numbers are written in base 10, rather than say in base 2. One good answer is: why not? We write numbers in base 10; is there a reason to hide that from the aliens? The whole point of the message is to tell the aliens a little bit about ourselves, so why disguise the fact that we use base-10 numerals? Another reason is that base-10 numbers are easier to proofread for the humans sending the message.

The third section of the page is a list of prime numbers from 2 to 89:

67, 71, 73, 79, 83

and finally the number !!2^{3021377}-1!!


which was the largest prime number known to humans at the time. (The minus sign and exponentiation notation are explained on later pages.) Why? Again. to tell the aliens about ourselves: here's a glimpse of the limits of our mathematical knowledge.

I often wonder what the aliens will think of the !!2^{3021377}-1!!. Will they laugh at how cute we are, boasting about the sweet little prime number we found? Or will they be astounded and wonder why we think we know that such a big number is prime?

The next article, to appear 2015-08-12, will discuss page 2, shown at right. (Click to enlarge.) Try to figure it out before then.

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Sun, 09 Aug 2015

A message to the aliens, part 0/23 (framing)

Earlier articles: Introduction

(At left is page 1 of the Cosmic Call message. For an enlarged version of the image, click it.)

First, some notes about the general format of each page. The Cosmic Call message was structured as 23 pages, each a 127×127 bitmap. The entire message was therefore 127×127×23 bits, and this would hopefully be suggestive to the aliens: they could try decoding it as 127 pages of 127×23-bit images, which would produce garbage, or as 23 pages of 127×127-bit images, which is correct. Or they might try decoding it as a single 127×2921-bit image, which would also work. But the choices are quite limited and it shouldn't take long to figure out which one makes sense.

To assist in the framing, each page of the message is surrounded by a border of black pixels and then a second smaller border of white pixels. If the recipient misinterpreted the framing of the bit sequence, say by supposing that the message was made of lines of 23 pixels, it would be immediately apparent that something was wrong, as at right. At the very least the regular appearance of the black border pixels every 127 positions, and the fact that the message began with 128 black pixels, would suggest that there was something significant about that number. If the aliens fourier-transform the message, there should be a nice big spike at the 127 mark.

Most of the message is encoded as a series of 5×7-pixel glyphs. The glyphs were generated at random and then subject to later filtering: candidate glyphs were discarded if they don't differ from previous glyphs in enough bit positions. This is to help the recipients reconstruct the glyphs if some of the bits are corrupted in transmission, as is likely.

The experimenters then eyeballed the glyphs and tried to match glyphs with their meanings in a way that would be easy for humans to remember, to aid in proofreading. For example, the glyph they chose to represent the digit 7 was .

People frequently ask why the message uses strange glyphs instead of standard hindu-arabic numerals. This is explained by the need to have the glyphs be as different as possible. Communication with other stars is very lossy. Imagine trying to see a tiny flickering light against the background of a star at a distance of several light years. In between you and the flickering light arevariable dist and gas clouds. Many of the pixels are likely to be corrupted in transmission. The message needs to survive this corruption. So glyphs are 35 bits each. Each one differs from the other glyphs in many positions, whereas a change of only a few pixels could change a standard 6 into an 8 or vice versa. A glyph is spread across multiple lines of the image, which makes it more resistant to burst errors: even if an entire line of pixels is destroyed in transit, no entire glyph will be lost.

At the top left and top right of each page are page numbers. For example, page number 1: The page numbers are written in binary, most significant bit first, with representing a 1 bit and representing a 0 bit. These bit shapes were chosen to be resistant to data corruption; you can change any 4 of the 9 pixels in either shape and the recipient can still recover the entire bit unambiguously. There is an ambiguity about whether the numerals are written right to left or left to right—is the number 1 or the number 16?—but the aliens should be able to figure it out by comparing page numbers on consecutive pages; this in turn will help them when time comes for them to figure out the digit symbols.

Every page has a topic header, in this case , which roughly means “mathematics”. The topics of the following pages are something like:

  • 1–5 Mathematics
  • 6–11,21 Physics
  • 12–14,19–20 The Earth
  • 15–18 Human anatomy and biochemistry
  • 22 Cosmology
  • 23 Questions

In the next article I'll explain the contents of page 1. Each following article will appear two or three days later and will explain another page.

To follow the whole series of articles in your feed reader, subscribe to: RSS Atom

Zip file of all 23 pages

(Next article, to appear 2015-08-10: page 1)

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Wed, 11 May 2011

A message to the aliens (introduction)
In 1999, two Canadian astrophysicists, Stéphane Dumas and Yvan Dutil, composed and sent a message into space. The message was composed of twenty-three pages of bitmapped data, and was sent from the RT-70 radio telescope in Yevpatoria, Ukraine, as part of a set of messages called Cosmic Call.

The message images themselves are extremely compelling. I saw the first one in the book Beyond Contact by Brian McConnell:

I didn't think much of the rest of the book, but the image was arresting. After staring at it for a while, and convincing myself I understood the basic idea, I found the full set of images on Mike Matessa's web site, printed them out, and spent a happy couple of hours at the kitchen table deciphering them.

Sometimes when I gave conference talks, I would put this image on the screen during break, to give people something to think about before the class started up again. I like to say that it's fun to see if you're as smart as an alien, or at least if as smart as the Canadian astrophysicists thought the aliens would be.

I invite you to try to understand what is going on in the first image, above. In a day or two I will post a full explanation, along with the second image. Over the next few weeks I hope to write a series of blog articles about the 23 pages, explaining the details of each.

If you can't wait that long for the full set, you can browse them here, or download a zip file.

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Fri, 15 May 2009

"Known to Man" and the advent of the space aliens
Last week I wrote about how I was systematically changing the phrase "known to man" to just "known" in Wikipedia articles.

Two people so far have written to warn me that I would regret this once the space aliens come, and I have to go around undoing all my changes. But even completely leaving aside Wikipedia's "Wikipedia is not a crystal ball" policy, which completely absolves me from having to worry about this eventuality, I think these people have not analyzed the situation correctly. Here is how it seems to me.

Consider these example sentences:

  • Diamond is the hardest substance known to man.
  • Diamond is the hardest substance known.

There are four possible outcomes for the future:

  • Aliens reveal superhardium, a substance harder than diamond.
  • Aliens exist, but do not know about superhardium.
  • The aliens do not turn up, but humans discover superhardium on their own.
  • No aliens and no superhardium.

In cases (1) and (3), both sentences require revision.

In case (4), neither sentence requires revision.

But in case (2), sentence (a) requires revision, while (b) does not. So my change is a potential improvement in a way I had not appreciated.

Also in last week's article, I said it would be nice to find a case where a Wikipedia article's use of "known to man" actually intended a contrast with divine or feminine knowledge, rather than being a piece of inept blather. I did eventually find such a case: the article on runic alphabet says, in part:

In the Poetic Edda poem Rígþula another origin is related of how the runic alphabet became known to man. The poem relates how Ríg, identified as Heimdall in the introduction, ...

I gratefully acknowledge the gift of Thomas Guest. Thank you!

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Thu, 27 Apr 2006

Most of the academic part of high school is mercifully gone from my memory, dissolved together into a uniform blur of dullness. I wrote recently about one question I remember fondly from one final exam. I only remember a few specific exam questions, and probably that is the only one I remember because it was such a good question.

The one exam question that sticks most clearly in my mind was from my eighth-grade science class: What color do you see if you look at a yellow light through a monochromatic red filter?

I said it would look red, and was marked wrong. I argued my answer with the teacher, Mr. Goodman, but he would not give me credit. I puzzled over this for a long time, and eventually understood what had happened.

The word "yellow" is not a designation of physics alone; it refers to a certain experience, and is a perceptual phenomenon, not a purely physical one. It's possible to phrase the question to avoid this, but the question was not phrased in that way; it was expressly phrased in perceptual terms. A person who was achromatopsic might see a yellow light through a monochomatic red filter in a very unusual way.

To bring up the possibility of achromatopsia in the context of an exam is just nitpicking; I mention it only to point out that the question, as posed, must involve a consideration of human perception. And the objection I raised at the time is certainly not just nitpicking, because there are two entirely different physical phenomena that both go by the name of "yellow". The confusion of these two things occurs in the human retina.

The perception of color is a very complicated business, and I can't explain it in complete detail today. Partly this is because it isn't understood in complete detail, partly because I don't know everything that is understood, and partly it is because this article is about something else, and I want to try to come to the point eventually. So all my assertions about color perception in this article should be taken as metaphors for what is really happening. Although they give a correct general idea of a perceptual process that is something like what actually occurs, they are not accurate and are not intended to be accurate.

With that warning in place, I will now explain human color perception. Color is sensed by special "cone cells" in the retina. Different cone cells are sensitive to different frequencies of photons. Cone cells come in three types, which we will call "red", "green", and "blue", although all three of these are misnomers to one degree or another. The "red" cone cells are sensitive to red and yellow photons; the "green" cone cells to yellow and green photons. We will ignore the blue cones.

Photons with a wavelength of around 570 nanometers stimulate both the red and the green cone cells, and this stimulation is eventually perceived as the color yellow. But you can stimulate the cone cells the same way without using any light with a frequency around 570 nm. If you bombard the retina with photons of 650 nm, you stimulate only the red cones, and the light looks red; if you bombard the retina with photons of 520 nm, you stimulate only the green cones, and the light looks green. If you bombard the retina with both kinds of photons at once, both the red and green cones are stimulated, just as they were by the 570 nm photons. They have no way to know that they are being stimulated by two different groups of photons instead of by the same group, so the perception is the same.

This is why your computer monitor and your television can display the color yellow, despite having no source of yellow light. The monitor has little red phosphors and little green phosphors. When it activates both of them at once, the red and green photons stream out and get into your eye, where they stimulate the red and green cones, and you perceive the color yellow.

But from a purely physical point of view, this "yellow" phenomenon is not at all like the one that occurs when you look at a lemon or at a sodium vapor street light. The photons coming off the lemon are all of about the same frequency, around 570 nm. The photons coming off the computer monitor picture of the lemon are two different frequencies, some around 520 nm, and some around 650 nm. Your eye is not equipped to tell the difference.

Now, suppose you are looking at "yellow light" through a monochromatic red filter that passes only 650 nm photons. What do you see?

Well, if it was monochomatic yellow light, say from a lemon, then you see nothing, because the filter stops the 570 nm photons. This was Mr. Goodman's exam answer.

But if it was the yellow light that comes from a television picture of a lemon, then it contains some 520 nm photons, which are stopped by the filter, and some 650 nm photons, which are not stopped. You would see a red lemon. This was my exam answer.

The perception of mixed red and green light as yellow was part of the curriculum that year---we had had a classroom demonstration of it---and so it was fair game for the exam. Mr. Goodman's exam question, as posed, was genuinely ambiguous. There are two physical phenomena that are both described as "yellow", and he could have meant either one.

This confusion of two distinct physical phenomena by the retina is something we take for granted, but it is by no means inevitable. I often imagine our meeting with the aliens, and their surprise when they learn that all of us, every human on earth, are color-blind. They will find this out quickly, as soon as they see a television or a computer monitor. "Your monitor is broken," Zxaxgr will say.

"It looks all right to me," replies Flash Gordon.

"Is there something wrong with your eyes? The color adjustment for yellow is completely off. It is coming out as redgreen instead of as yellow."

"I see nothing wrong with the color adjustment for yellow," replies Flash.

"There must be something wrong with your eyes."

And yes, Zxaxgr is right. There is something wrong with our eyes. There is an intrinsic design flaw in our computer monitors, none of which can display yellow, and we don't care, because none of us can tell the difference between redgreen and yellow.

To empathize with Zxaxgr's puzzlement, imagine how strange it would be to learn that the alien televisions cannot display green; they display purple instead: purple trees, purple broccoli, purple frogs, purple flags of Saudi Arabia. And the aliens have never noticed the problem. You want to ask them about it, but your English-to-Alien dictionary doesn't have an entry for "purple". When you ask them about it, they say you're nuts, everything looks green, as it should. You learn that they have no word for purple; they just call it green, and eventually you find out that it's because they can't tell the difference between purple and green.

Whatever you're thinking now, that's what Zxaxgr is going to think.

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Sat, 18 Mar 2006

Mysteries of color perception
Color perception is incredibly complicated, and almost the only generalization of it that can be made is "everything you think you know is probably wrong." The color wheel, for example, is totally going to flummox the aliens, when they arrive. "What the heck do you mean, 'violet is a mixture of red and blue'? Violet is nothing like red. Violet is less like red than any other color except ultraviolet! Red is even less like violet than it is like blue, for heaven's sake. What is wrong with you people?"

Well, what is wrong with us is that, because of an engineering oddity in our color sensation system, we think red and violet look somewhat similar, and more alike than red and green.

But anyway, my real point was to note that the colors in look a lot different against a gray background than they do against the blue background in the bar on the left. People who read this blog through an aggregator are just going to have to click through the link for once.

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Fri, 17 Mar 2006

More on Emotions
In yesterday's long article about emotions, I described the difficulty like this:

There's another kind of embarrassment that occurs when you see something you shouldn't. For example, you walk into a room and see your mother-in-law putting on her bra. You are likely to feel embarrassed. What's the connection with the embarrassment you feel when you fall off a ledge? I don't know; I'm not even sure they are the same. Perhaps we need a new word.

This morning I mentioned to Lorrie that the idea of "embarrassment" seemed to cover two essentially different situations. She told me that our old friend Robin Bernstein had noticed this also, and had suggested that the words "enza" and "zenza" be used respectively for the two feelings of embarrassment for one's self and for embarrassment for other people.

I also thought of another emotion that was not on my list of basic emotions, but seems different from the others. This emotion does not, so far as I know, have a word in English. It is the emotion felt (by most people) when regarding a happy baby, the one that evokes the "Awwww!" response.

This is a very powerful response in most people, for evolutionarily obvious reasons. It is so powerful that it is even activated by baby animals, dolls, koala bears, toy ducks, and, in general, anything small and round. Even, to a slight extent, ball bearings. (Don't you find ball bearings at least a little bit cute? I certainly do.)

The aliens might or might not have this emotion. If they are aliens who habitually protect and raise their young, I think it is inevitable. The aliens might be the type to eat their young, in which case they probably will not feel this way, although they might still have that response to their eggs, in which case expect them to feel warmly about ball bearings.

I also gave some more thought to Ashley, the Pacemate who claimed that her most embarrassing moment was crashing into the back of a trash truck and totaling her car. I tried to understand why I found this such a strange response. The conclusion I finally came to was that I had found it inappropriate because I would have expected fear, anger, or guilt to predominate. If Ashley is in a vehicle colision severe enough to ruin her car, I felt, she should experience fear for her own safety or that of others, anger at having wrecked her car, guilt at having carelessly damaged someone else's property or health. But embarrassment suggested to me that her primary concern was for her reputation: now the whole world thinks that Ashley is a bad driver.

If you don't see what I'm getting at here, the following situational change might make it clearer:

Most Embarrassing moment

Ashley (alternate universe version): Crashing into the back of a school bus full of kids and totaling my car!

You almost crippled seventy schoolkids? Gosh, that must have been embarrassing!

Having made the analysis explicit for myself, and pinned down what seemed strange to me about Ashley's embarrassment, it no longer seems so strange to me. Here's why: It wasn't a school bus, but a garbage truck. Garbage trucks are big and heavy. The occupants were much less likely to have been injured than was Ashley herself, partly because they were in a truck and also because Ashley struck the back of the truck and not the front. The truck was almost certainly less severely damaged than Ashley's car was, perhaps nearly unscathed. And of course it was impossible that the truck's cargo was damaged. So a large part of the motivation for fear and guilt is erased, simply because the other vehicle in the collision was a garbage truck. I would have been angry that my car was wrecked, but if Ashley isn't, who am I to judge? Probably she's just a better person than I am.

But I still find the reaction odd. I wonder if some of what Ashley takes to be embarrassment isn't actually disgust. But at least I no longer find it completely bizarre.

Finally, thinking about this led me to identify another emotion that I think might belong on the master list: relief.

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Thu, 16 Mar 2006

I was planning to write another article about π, and its appearance in Coulomb's law, or perhaps an article about how to calculate the volume of a higher-dimensional analogue of a sphere.

But John Speno says he always skips the math stuff on my blog, and the last couple of days have been unrelievedly mathematical. So instead, John, I have written an article about the comparison of emotions, whether the 18-toed Sirian ghost worms will understand why you are holding your nose, Homer Simpson, the evolutionary justification for disgust, the Indiana Pacers cheerleading squad, Paris Hilton, and maggots. Skip this, I dare you.

My shrink had a little trope that she'd trot out when she asked me how I had felt about something and I wasn't sure. "Mad, sad, glad, scared," she'd say, and that was helpful, because those four do cover an awful lot of situations. And learning to recognize those four is very important.

But one day she pushed the idea too far and asserted that those were the only emotions there are.

That's clearly wrong. Even discounting emotions that might be considered variations on the big four, such as: (anger) rage, annoyance, resentment, frustration, (sadness) grief, disappointment, remorse, loneliness, (happiness) delight, joy, pride, (fear) nervousness, dread, terror, panic, and so on, we still have:

  • Boredom
  • Disgust
  • Envy
  • Guilt
  • Jealousy
  • Lust
  • Shame
  • Surprise
It's funny that a shrink would forget about guilt, but there you are.

Some of these may require explanation. People sometimes use the word "disgust" metaphorically to refer to a feeling that is really nine parts anger to one part boredom, as when they say they are disgusted with the state of American politics. But that's not what I mean by it here. The disgust I'm referring to is the feeling you have when you have been on vacation and come back to discover that the power went out while you were away and the meat in the refrigerator has spoiled and slid out onto the kitchen floor where it is now festering with thousands of squirming, white, eyeless maggots, and the instant you see it, your reaction is to (a) turn away, (b) hold your nose, and (c) vomit. I suppose it's possible that some people would have that very reaction to American politics; it's certainly understandable. But I don't think that's what people usually mean when they say that politics disgusts them. Or if they do mean it, they mean it only in a hyperbolic sense.

People often confuse guilt and shame, but they are really orthogonal. You feel guilt when you have done something you believe is ethically or morally wrong. You feel shame when other people observe you doing something that they shouldn't see, whether or not that thing is ethically or morally wrong. The problem is with the observing, not with the thing that is being observed. I think the following example will help clear up the confusion: One might or might not feel guilty about picking one's nose, although I think most people don't feel guilty when they do it. But even someone who picks their nose entirely without guilt, probably feels ashamed if someone else catches them in the act.

The other two that are often confused are envy and jealousy. Here I think the confusion is caused simply because people don't know what the words mean. Envy is what you feel when you want what someone else has; you can envy someone else's car or their lunch or their special relationship with their lover. Jealousy is much more specific. You are jealous when you have a special relationship with a person, and you are afraid that you are going to lose them to a third person. You can envy someone else's possession of a ham sandwich, but jealousy of a ham sandwich is impossible.

I might be willing to believe the proposition these eight, plus the original four (anger, sadness, happiness, and fear) constitute a complete set of "primary colors" for human emotion, and that you can consider the others as being mixtures of various amounts of these twelve. For example, you go up on stage to accept an award, and your trousers fall off, and you feel embarrassed. What is embarrassment? It's maybe five parts shame, two parts fear, and one part surprise. Take away any of these three things, and you no longer have embarrassment, but something else. Add in anger and you have humiliation.

If someone wants to argue that jealousy is compounded from fear, anger, and envy, and should be removed from the list in favor of affection or confusion, I won't complain. The list is necessarily dependent on culture, and even more so on the individual making it. Not every culture will have anything like jealousy; perhaps most won't. Romantic love seems to be a uniquely European invention, dating from around the 13th century.

Another problem with the list is that even within one culture, there may not be agreement on which kinds of feelings qualify as emotions. Does hunger qualify? Or fatigue? It seems to me that some emotions are more rooted in the physical processes of the body, and others less so. Guilt is at the "high" end of that scale: it refers to a feeling you have in your mind when you have done something that you feel you shouldn't have. It is hardly associated with the body at all. A brain in a vat could feel guilt, and probably does. At the "low" end of the scale is disgust, the experience of which is much less about an the social constructions in your mind than it is about your stomach trying to turn itself inside out. I think hunger and fatigue are even farther down the scale of body-vs-mind than disgust; below even those is pain, and at the very bottom are feelings like the one you have in your arm when you open a door, which is purely physical and has no emotional content whatsoever. The counterparts at the top end of the scale are plans, analyses, and the like, which are purely mental and have no emotional content. Emotion is somewhere in between, and I can imagine that someone else could want to exclude disgust or guilt from a list of emotions because they were too far down from the middle of the scale.

An exercise I love to do is to try to consider what we will have in common with the space aliens. For example, do the space aliens consider the P=NP problem interesting? Do the space aliens consider the set of real numbers as a fundamental object, or as an obscure construction only of interest to set theorists? I will probably address these topics in future articles. Meanwhile, this article, believe it or not, started out as a discussion of whether the space aliens, when they arrive, will already know how to play chess. (Well, obviously not. But it is less obvious that they will not already know how to play go. I will write that article sooner or later.)

But now we might ask what kinds of emotions the aliens will have. The question seems at first glance to be completely impossible. But I believe that partial answers are possible.

As emotions get higher up on the body-to-mind scale, it becomes less likely that they will be shared by the aliens; such emotions are not even cross-cultural among humans. Our experience of guilt is very much dependent on our culture, and in particular on our relationship to law and authority, much of which is the result of two thousand years of Christian philosophizing. The converse is that emotions that are low on the body-to-mind scale are much more universal among people. Perhaps not everyone feels guilt. But everyone feels disgust.

Disgust is particularly easy to analyze from the point of view of natural selection. It is to a large extent an aversion to dangerous biohazards: rotten food and carcasses; decay, including mold, and things that look like mold; excrement, vomit, and other body substances that should be inside but that have come out; disembowelment and bodily mutilation; deformity and disease. Rotting meat is extremely poisonous, so an automatic aversion reaction makes evolutionary sense: the people who turned away in disgust lived longer than the people who saw an opportunity for a free lunch. Excrement, and particularly human excrement, harbors bacteria dangerous to humans, so an automatic aversion reaction makes evolutionary sense. Deformity is similar. Perhaps whatever caused it is not contagious—but perhaps it is, and evolution wants to stay on the safe side.

I think it is inevitable that the aliens will have these same kinds of reactions, for the same reasons. Aliens will have a strong aversion reaction if you put them in front of a chunk of rotting alien flesh, or show them an alien with its internal organs on the outside. Why? Because those things are dangerous to aliens, and so all the aliens who didn't have that reaction have died long ago of horrible diseases. I don't think it's a big step to identify this reaction with disgust.

Similarly, aliens might not have eyes, if they come from a place with no ambient short-wavelength electromagnetic radiation; say, the surface of Jupiter. But the aliens will have chemical senses, analogous to smell and taste, because there are chemicals everywhere. Every life form on earth has chemical senses, even down to bacteria. This is because you cannot use the Homer Simpson strategy of ingesting everything you encounter; you would quickly die. (Homer is fictitious, or he would be dead long ago.) You need some way of distinguishing which items are food, so that you can eat the things that are food and ignore the other things. So you need to have a sense of smell and taste.

What happens when you smell or taste something that is really harmful? You had better have some kind of aversion reaction, and you do, because all the 18-toed Sirian ghost worms without those reactions ate stuff that disagreed with them, and died young; you are the product of a long line of ghost worms that do have a sense of smell and feel disgust when they wander into a biohazard zone.

We can push this even further. I conjecture that we can even predict some of the aliens' body language. When presented with something that smells bad—say rotten food—an alien's response will be to hold its nose, if it has an olfactory sense that can be disabled by closing the organ off from the outside world. If the alien asks me what I think of Paris Hilton, and I hold my nose, the alien will understand that Paris Hilton is being insulted, and will understand something of the way in which Paris Hilton is being insulted. Chemical senses, I think, must be so universal that even noseless aliens will understand the gesture, once the structure and function of the human nose is explained to them. "Oh, I see," says the alien. "You have closed off your chemical sense organ so that Ms. Hilton's noxious effluvia cannot penetrate. Yes, I quite understand! Unfortunately, for us it is not possible since our olfactory bulbs are distributed throughout our skins. But I am sure we have all wanted to do something like that at one time or another."

Disgust, being one of the lowest emotions on the mind-body scale, is one of the easiest to attribute to the aliens. Even going a little higher is risky. Will the aliens feel lust? Quite possibly. Even a giant amoeba that reproduces by fission might feel something akin to lust when the time comes, a powerful urge to divide in two. Will the aliens feel anger? Perhaps, but here we're on shaky ground.

Long ago, I had a conversation with Matthew Stone, in which he told me how different cultures have different notions of even apparently simple emotions such as rage. Rage, he said, is characterized by the following situation: you want something, but there is some insurmountable obstacle to your getting it, and so you are frustrated. When you become enraged, your response is to attack the obstacle and try to destroy it.

But, said M. Stone, in Polish, when you want something, and there is an insurmountable obstacle, and you are frustrated, you do not have a fit of rage in which you go nuts and attack the obstacle. Instead, you have a fit of złost, in which you go nuts and attack everything around you at random.

Or, in some other culture that I forget, if you want something to which there is an insurmountable obstacle, and you are frustrated, then you have a fit of some emotion I don't remember the name of, in which you go nuts and kill yourself.

These seem to me to be distinctly different from rage, if not fundamentally so. Variations on jealousy are even easier to invent.

I don't know how much of all this is true, how much was wrong before M. Stone heard it, how much he said that was right but I misunderstood, and how much I understood correctly but got wrong between then and now. It might all be nonsense. But one can still get some mileage out of attributing złost, rather than rage, to the aliens.

Embarrassment is another one of the more universal emotions. I've seen my cat act embarrassed, typically when he falls off of a ledge, or tries to jump from A to B but only makes it partway, and goes splat.

There's another kind of embarrassment that occurs when you see something you shouldn't. For example, you walk into a room and see your mother-in-law putting on her bra. You are likely to feel embarrassed. What's the connection with the embarrassment you feel when you fall off a ledge? I don't know; I'm not even sure they are the same. Perhaps we need a new word.

The Indiana Pacers basketball team has a web site on which they list the "most embarrassing moments" of each of their cheerleaders, the Pacemates. (I keep wanting to call them the "Pacemakers", but even I know that is wrong.)

When I first planned to discuss this, it was because my random sample of responses picked up mostly strange ones, and I was ready to conclude that the Pacemates and I were not of the same species. I planned to complain that none of the Pacemates had apparently ever farted in public. But a more thorough survey revealed that the Pacemates were much less surprising in their embarrassment than I had originally thought. As embarrassing moments go, you would be hard-pressed to find a more typical example than that of falling down in the middle of a carefully-choreographed public dance exhibition, and that is mostly what they said. Both I and my cat can understand the embarrassment of these mishaps:

Lindsay: I usually don't get embarrassed, but one time, I did fall off stage at a national dance competition.

Darcy: Last year during Pacers player introductions when the lights were out, Boomer ran into me and knocked me down to the floor!

Amanda: When I was cheering at an IU game, I went back for a back handspring and in the middle of Assembly Hall court, I landed flat on my head.

Kim: When I was in sixth grade, I slipped and fell on the ice trying to get on the school bus. I had on a skirt and dress shoes and was carrying my trumpet!

I don't know what the trumpet has to do with it, but my cat and I can sympathize with the part about slipping on the ice while trying to board the school bus.

I find it rather comforting that the Pacemates are embarrassed by the same things that embarrass me or my cat or both. I had been worried that all the embarrassing moments would be strange and puzzling, like this one:

Ashley: Crashing into the back of a trash truck and totaling my car!
Items like this had made me wonder if the author and I were using the word in the same way. But for the most part I felt that I could understand and empathize, and when I looked at the complete list, I was delighted to discover just what I had asked for:

Nikki: During speech class of my freshman year of college, I was giving a speech on the health care industry and I...well, let's just say for the rest of the semester, my classmates nicknamed me "Toot-Toot!"

There is a crucial scene in Larry Niven's novel World of Ptavvs about embarrassment among aliens. Kzanol is an alien invader. In order to escape from Kzanol's telepathic control, the protagonist, Larry Greenberg, must understand how the aliens shield themselves from each others' commands. He has access to Kzanol's memories, and finds the memory he wants in an episode from Kzanol's childhood in which Kzanol involuntarily defecated in front of his father's houseguests. I'm sure that Pacemate Nikki would sympathize.

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